| A three-dimensional model for diffusionless phase transitions in solids (e.g., martensitic transitions, twinning) is proposed. The model provides a constitutive description for interfaces that divide a body into bulk parts with distinct constitutive behavior. The interfaces are thin, but smooth, mobile, transition zones, whose configuration alters with deformational load and with orientation. Interface propagation is associated with energy dissipation, and the mobility of the transition layers varies with the interfacial deformation gradient, orientation, and velocity.; An asymptotic analysis, in the limit of vanishing interfacial thickness, demonstrates that the order-parameter based theory is completely consistent with a recent, well-established, sharp-interface theory in which phase interfaces are represented by surfaces of discontinuity. As a result of the asymptotic analysis, it is concluded that the proposed model may actually serve as a successful regularization of the sharp-interface theory. Conversely, the analysis may be interpreted as an independent derivation of the sharp-interface theory appropriate to the problem at hand.; A series of computational simulations concerned with the formation and evolution of deformation twins in a single crystal are performed using the aforementioned model. The relevant algorithm employs a spectral method in space, with a resolution enhancement option, and an adaptive third-order Runge-Kutta method in time. The results of computational and analytical studies reveal pertinent information about nucleation and growth kinetics. To model microstructural refinement, a constitutive theory that incorporates a length-scale associated with the characteristic size of microstructure is developed. |
